JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 24 February 2021, Shift 1, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

f : \mathbb{R} \to \mathbb{R}

is a function defined by

f(x) = [x - 1]\cos\left(\frac{2x - 1}{2}\right)\pi

, where

[\cdot]

denotes the greatest integer function, then

f

is :

(1)discontinuous only at $x = 1$
(2)discontinuous at all integral values of $x$ except at $x = 1$
(3)continuous only at $x = 1$
(4)continuous for every real $x$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity involving GIF and Fractional Part

Same idea in other shifts

Asked 17× in all

2 Apr 2026, Shift 2 · Q25The number of points in the interval $[2, 4]$ , at which the function $f(x) = x^2 - x - \frac{1}{\lfloor x \rfloor - \frac{1}{2}}$ , where…MediumNumerical value
5 Apr 2024, Shift 2 · Q10Let $f : [-1, 2] \to \mathbf{R}$ be given by $f(x) = 2x^2 + x + [x^2] - [x]$ , where $[t]$ denotes the greatest integer less than or equal…MediumSingle correct
6 Apr 2024, Shift 2 · Q24Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f:[0,\infty)\to\mathbb{R}$ be a function defined by…MediumNumerical value
27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
6 Apr 2023, Shift 1 · Q25Let $a\in\mathbb{Z}$ and $[t]$ be the greatest integer $\le t$ . Then the number of points, where the function $f(x)=[a+13\sin x]$ ,…HardNumerical value
11 Apr 2023, Shift 1 · Q7Let $f(x) = [x^2 - x] + |-x + [x]|$ , where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ isMediumSingle correct
12 Apr 2023, Shift 1 · Q25Let $[x]$ be the greatest integer $\le x$ . Then the number of points in the interval $(-2,1)$ , where the function…MediumNumerical value
29 Jul 2022, Shift 2 · Q26If $[t]$ denotes the greatest integer $\leq t$ , then the number of points, at which the function…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.